Properties of multivariate beta distributions

ABSTRACT: Let 1 1 , ..., X Xr + be independent random variables, ~ Ga( , ), Xi ai θi i = 1, ..., r +1. Define Y X (X X ) i r i i i r , 1, ..., = + +1 = and , Zi = Xi Xr+1 i = 1, ..., r. Then, ( ) Y Yr , ..., 1 and ( ) Z Zr , ..., 1 follow multivariate beta type 1 and type 2 distributions, respective...